Fermi Edge Singularities in the Mesoscopic Regime: I. Anderson Orthogonality Catastrophe

TL;DR

This paper investigates the Anderson orthogonality catastrophe in mesoscopic systems, revealing that AOC is incomplete and exhibits broad distributions due to mesoscopic fluctuations, with analytic expressions derived for strong perturbations.

Contribution

It provides a novel analytic description of AOC overlaps in mesoscopic systems using a random matrix model, highlighting the effects of finite size and fluctuations.

Findings

AOC is incomplete in mesoscopic systems with discrete energy levels.

Fluctuations cause a broad distribution of AOC overlaps.

Analytic expressions are derived for strong perturbations.

Abstract

For generic mesoscopic systems like quantum dots or nanoparticles, we study the Anderson orthogonality catastrophe (AOC) and Fermi edge singularities in photoabsorption spectra in a series of two papers. In the present paper we focus on AOC for a finite number of particles in discrete energy levels where, in contrast to the bulk situation, AOC is not complete. Moreover, fluctuations characteristic for mesoscopic systems lead to a broad distribution of AOC ground state overlaps. The fluctuations originate dominantly in the levels around the Fermi energy, and we derive an analytic expression for the probability distribution of AOC overlaps in the limit of strong perturbations. We address the formation of a bound state and its importance for symmetries between the overlap distributions for attractive and repulsive potentials. Our results are based on a random matrix model for the chaotic conduction electrons that are subject to a rank one perturbation corresponding, e.g., to the localized core hole generated in the photoabsorption process.